I
describe our recent work in generating exotic entangled states a
sample of laser-cooled atomic spins. We use quantum non-demolition
(QND) measurement techniques [1] to prepare entangled spin states. In
the simplest case, we measure a single spin component and generate
spin-squeezing in a sample of highly polarised atoms - a useful
resource for quantum-enhanced atomic magnetometry [2]. More recently,
we have developed techniques for squeezing all three spin components
of an unpolarised sample of atoms. This generates a highly entangled
macroscopic spin singlet (MSS) [3,4], analogous to the ground state
of many fundamental spin models in condensed matter physics. The
state we generate is SU(2) invariant, so it is directly useful for
background-free measurement of magnetic field gradients, and may be
useful for quantum information tasks such as storing information in a
decoherence free subspace. Combining this with quantum feedback
control [5] should allow us to deterministically prepare a MSS. In
the outlook I discuss prospects for using these techniques for
quantum state engineering of quantum lattice gases [6].